A method of calculating numerically the optical transfer function appropriate to any type of image motion and vibration, including random ones, has been developed. Here, the numerical calculation method is compared to experimental measurement, and the close agreement justifies implementation in image restoration for blurring deriving from any type of image motion. In addition, statistics regarding limiting resolution as a function of relative exposure time for low frequency vibrations involving random blur are described. An analytical approximation to the probability function has been obtained. This can be implemented in target acquisition probability. Comparison of image quality is presented for three different kinds of motion: linear, acceleration, and high frequency vibration for the same blur radius. The parameter considered is the power spectrum of the picture.